High order edge elements on simplicial meshes
Rapetti, Francesca
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 41 (2007), p. 1001-1020 / Harvested from Numdam
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Low order edge elements are widely used for electromagnetic field problems. Higher order edge approximations are receiving increasing interest but their definition become rather complex. In this paper we propose a simple definition for Whitney edge elements of polynomial degree higher than one. We give a geometrical localization of all degrees of freedom over particular edges and provide a basis for these elements on simplicial meshes. As for Whitney edge elements of degree one, the basis is expressed only in terms of the barycentric coordinates of the simplex.

Publié le : 2007-01-01
DOI : https://doi.org/10.1051/m2an:2007049
Classification:  78M10,  65N30,  68U20 
@article{M2AN_2007__41_6_1001_0,
     author = {Rapetti, Francesca},
     title = {High order edge elements on simplicial meshes},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {41},
     year = {2007},
     pages = {1001-1020},
     doi = {10.1051/m2an:2007049},
     mrnumber = {2377104},
     zbl = {1141.78014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2007__41_6_1001_0}
}

Rapetti, Francesca. High order edge elements on simplicial meshes. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 41 (2007) pp. 1001-1020. doi : 10.1051/m2an:2007049. http://gdmltest.u-ga.fr/item/M2AN_2007__41_6_1001_0/

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